Demystifier said:
Heisenberg is still right in the sense that you cannot STRONGLY measure both position and momentum. But you can do it WEAKLY.
Yes, the HUP principle still applies and always will. As I understand it, Heisenberg was one of the most vocal of opponets to deBB Theory, due to his understanding that particle position can never be completely determined. Essentially, I believe Bohmian Mechanics uses the exact position of the particle as a NON-LOCAL Hidden variable, and of course, the HUP prevents that from ever being completely known, so one can only come close, and the Non-Local Hidden Variable of exact position will always remain hidden to the extent HUP demands.
The nice thing is, de Broglie-Bohm theory resolves Schrodinger's problem, where he complained his wave formula predicts a wave spread out over the detecting screen and he sees particles impacting the screen in little specks. John Bell was very clear that Bohmian Mechanics, or deBB if you want to give proper recognition to the genius of Luis de Broglie, turns the indeterminate statistical QM into a determinate process, eliminating the mysticism of the observer's special position in the Statistical QM and thereby doing away with the Copenhagen interpretation. This does not mean that statistical QM is invalid. Both theories use Schrodinger's Wave Equation and if deBB theory is valid then statistical QM must also be valid. In a sense, it just means that the moon is there, even if we aren't looking at it, and it took a specific trajectory to get where it is.
Of course, we can't measure the exact positions and momentum of individual photons to experimentally verify their trajectories are just as deBB theory predicts due to the HUP restrictions, so there is a limit to how much we can know about the trajectory of anyone particle, which is very little actually. But, by making measurements on 31,000 photons, and gaining just a little information off each, we can see the average trajectory is precisely what deBB theory predicts.
It's all explained here:
http://plato.stanford.edu/entries/qm-bohm/
If you look at the deBB predicted photon trajectories in figure 1. of the above referenced article, and look at the average trajectories measured by this experiment, you get an exact match. In hindsight, it seems all so obvious. The only mystery is why it took so long for this approach to be accepted. Especially when someone with the stature of John Bell was practically shouting from the rooftops that we should look at deBB theory more closely:
(Bell 1987, p. 160):
"But in 1952 I saw the impossible done. It was in papers by David Bohm. Bohm showed explicitly how parameters could indeed be introduced, into nonrelativistic wave mechanics, with the help of which the indeterministic description could be transformed into a deterministic one. More importantly, in my opinion, the subjectivity of the orthodox version, the necessary reference to the ‘observer,’ could be eliminated. ... "
Perhaps the first step in good science is to dispel mysticism. deBB theory dispels the mysticism of the observer's special position in the Copenhagen interpretation. The Copernican Principle holds. Ding dong, the witch is dead.
As usual, the above is my own humble opinion. Feel free to correct me if I have made a mistake.
